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The objective is to minimize the <jats:italic>makespan<\/jats:italic> of the motion schedule, i.e., to reach the new configuration in a minimum amount of time. We show that this problem is -complete, even for deciding whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved. On the algorithmic side, we establish simultaneous constant-factor approximation for two fundamental parameters, by achieving <jats:italic>constant stretch<\/jats:italic> for <jats:italic>constant scale<\/jats:italic>. Scaled shapes (which arise by increasing all dimensions of a given object by the same multiplicative factor) have been considered in previous seminal work on self-assembly, often with unbounded or logarithmic scale factors; we provide methods for a generalized scale factor, bounded by a constant. Moreover, our algorithm achieves a <jats:italic>constant stretch factor<\/jats:italic>: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of <jats:italic>d<\/jats:italic>, then the total duration of our overall schedule is <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {O}(d)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which is optimal up to constant\u00a0factors.<\/jats:p>","DOI":"10.1007\/s10458-023-09626-5","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T05:03:13Z","timestamp":1697518993000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Connected coordinated motion planning with bounded stretch"],"prefix":"10.1007","volume":"37","author":[{"given":"S\u00e1ndor P.","family":"Fekete","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Phillip","family":"Keldenich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ramin","family":"Kosfeld","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Rieck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Scheffer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,17]]},"reference":[{"issue":"4","key":"9626_CR1","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1109\/TASE.2015.2470096","volume":"12","author":"A Adler","year":"2015","unstructured":"Adler, A., de Berg, M., Halperin, D., & Solovey, K. 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